Subharmonic solutions with prescribed minimal period of a discrete forced pendulum equation
type: Item
instance of: scholarly article
title: Subharmonic solutions with prescribed minimal period of a discrete forced pendulum equation
zbMATH Open document ID: 1067.39022
author: Yuhua Long
author: Zhiming Guo
author: Jianshe Yu
published in: Journal of Dynamics and Differential Equations
publication date: 2005-03-15T00:00:00Z
review text: Using variational methods the authors obtain sufficient conditions on the existence of sub-harmonic solutions with prescribed minimal period \(pT\) for the second order difference equation \[ x(n+1)-2x(n)+x(n-1)+A \sin(x(n))=f(n),\quad f(n+T)=f(n). \] An example is given. The idea of the paper is to find variational functionals to transfer the existence of sub-harmonic solutions into the existence of critical points of the corresponding functional. This reviewer likes to add that the matrix \(B\) on page 579 in the paper is a circulant matrix some of its properties are well known [\textit{S. Barnett}, Matrices: Methods and applications, Oxford University Press (1990; Zbl 0706.15001)].
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 70J35
zbMATH DE Number: 2145903
zbMATH Keywords: second order difference equation
zbMATH Keywords: periodic solution
zbMATH Keywords: subharmonic solution
zbMATH Keywords: critical point
zbMATH Keywords: minimal period
zbMATH Keywords: discrete forced pendulum equation
reviewed by: Ahmed Hegazi
MaRDI profile type: Publication
full work available at URL: s10884-004-4292-2
OpenAlex ID: W2023620255
Wikidata QID: Q115383618
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DOI: 10.1007/S10884-004-4292-2
description: scientific article; zbMATH DE number 2145903